Optimal issuing policies for some particular classes of perishable inventory problems are derived under several possible objective functions. The inventory considered is one in which stock is grouped into categories according to shelf age. Demand occurs for each of the categories, and may be satisfied by inventory units from that category or from any “younger” category. It is shown for most of the objective functions considered that the optimal policy is to issue the oldest unit which will satisfy the demand. A prime example of the classes of inventory problems considered in this paper is the issuance of whole blood from a hospital or central blood bank.